Yoma 6:5-6

At every booth, the one leading the goat was offered food and water. [If he had to eat, it was permitted, but reportedly this was never necessary.] The person staffing each booth would accompany him to the next booth except for the last one; he did not accompany him to the cliff. Rather, he would stand and watch from a distance.

Yoma 6:6

When he reached the cliff, he divided the crimson thread, tying half to the rock and half between the goat’s horns. He pushed the goat backwards and it rolled down; it was dashed to pieces before it reached half-way down. He returned and sat in the last booth until night fell. At what point did his clothes become ritually unclean? As soon as he left the walls of Jerusalem. Rabbi Shimon says from the moment he pushed the goat off the cliff.